Summary

Let G be the formal generator of a d-dimensional stochastic gradient system associated to an interaction potential U. If ∫ G ϕ d μ= 0 for such smooth ϕ that G ϕ IL1(μ), then certain moment conditions imply that μ is a Gibbs random field for U. If U satisfies a stability condition, and d≦2 or μ is translation invariant, then these moment conditions can be replaced by a natural support condition. Results of Holley and Stroock [6] are extended to certain unbounded spin systems.